For small cuts: check your aim with a line on the shaft that runs through both contact points.
Drag the balls or click a pocket.
shot lineghost ballcuepaths that pocket
At the table
Judge x: the object ball's contact point's distance from its center.
Drop onto the shot line, tip at the cue ball's center.
Picture a line on the shaftx to the inside: its left side for a cut to the left.
Check that it runs through the cue ball's contact point (x inside its center) and on through the object ball's. Adjust until it does.
Looking down the cue
The check, looking down the cue. Green: the check line, x inside the cue's center. It runs through the cue ball's hidden contact point and the object ball's. Dashed: the cue's line, 2x from the object ball's center.
Where the check line sits on the shaft, looking at the tip end on. The circle is the tip; the green line is offset x from center.
How it works
Exact in principle. The line through the two contact points is parallel to the shot line and x = R·sin(cut) to the inside of it. With the cue on the shot line, a line on the shaft x to the inside runs through both points. At the object ball, that means the cue passes 2x from the object ball's center, so the check is double the distance judged along the cue.
Range. The check line stays on the shaft while x is less than the tip's radius. For a 13 mm tip that's cuts up to about 13°. Beyond that the line falls outside the shaft and you're back to judging a parallel line in space.
Pure geometry. These pages draw the ideal lines. Two things shift real shots: throw, friction between the balls that pushes the object ball slightly toward the thick side, and perspective, your eye misjudging distances on the balls depending on where you look from. Players learn to adjust for both with practice.